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International Journal of Wireless & Mobile Networks (IJWMN) Vol. 4, No. 6, December 2012

DOI : 10.5121/ijwmn.2012.4605 61

ANALYTICAL MODEL FORMOBILE USER

CONNECTIVITY IN COEXISTING

FEMTOCELL/MACROCELL NETWORKS

Saied M. Abd El-atty1

and Z. M. Gharsseldien2

1Department of Computer Science and Information, Arts and Science College,

Salman Bin Abdulaziz University, 54-11991,Wadi Adwassir, Kingdom of Saudi [email protected]

2Department of Mathematics, Arts and Science College, Salman Bin Abdulaziz

University, 54-11991,Wadi Adwassir, Kingdom of Saudi [email protected]

ABSTRACT

In this paper we investigate the performance of mobile user connectivity in femtocell/macrocell networks.The femto user equipment (FUE) can connect to femto access point (FAP) with low communication range

rather than higher communication range to macro base station (MBS). Furthermore, in such emerging

networks, the spatial reuse of resources is permissible and the transmission range can be decreased, then

the probability of connectivity is high. Thereby in this study, we propose a tractable analytical model for

the connectivity probability based on communication range and the mobility of mobile users in

femtocell/macrocell networks. Further, we study the interplays between outage probability and spectral

efficiency in such networks. Numerical results demonstrate the effectiveness of computing the connectivity

probability in femtocell/macrocell networks.

KEYWORDS

Femtocell, Macrocell, Connectivity, Mobility, Communication range.

1.INTRODUCTION

Integration of femtocell technology with the existing macrocell mobile networks is a promising

solution not only to improve indoor coverage but also to increase capacity of cellular mobilenetworks. Therefore, the deployment of femtocells technology will be useful for both users and

mobile network operators, since femtocell networks introduce better quality wireless services

and data transmission. Furthermore, the users make use of femtocell networks to receive strongsignals, and high capacity, as well as low transmission range and power wasting [1]. As a result,

the mobile network operators will have the solutions for radio resources limitations, reduction

macrocell traffic load and infrastructure cost by saving lots of money by offloading most of thecapital expenditure (CAPEX) and operational expenditure (OPEX) onto users [2].

In femtocell networks, the smaller size of femtocell not only provides high spectrum efficiencyby using spatial reuse of resources but also decreases the transmission range and then provides

high probability of connectivity.

The permanent address of the authors is1The Dept. of Electronics and Electrical Communications,

Faculty of Electronic Engineering, Menoufia University, 32952, Menouf, Egypt.2The Dept. of Math., Fac. Sci., Al-Azhar Uni., Nasr City,11884, Cairo, Egypt

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Further, one of the most important reasons for deployment femtocells technology is to serve theremote areas with no coverage or poor signal as well as to reduce the traffic volume on the

macrocell. Hence in this study, we introduce a mathematical model for the probability ofconnectivity as a function of communication range and the mobility of mobile user infemtocell/macrocell network. As well as, in terms of connectivity probability, we study the

interplays between the outage probability and the spectral efficiency based-signal to interference

ratio (SIR) in such networks.

The rest of the paper is organized as follows. The related work which discussed the technicalchallenges associated with femtocell deployment is presented in Section 2. Femtocell access

methods comparisons are investigated in Section 3. Then, the main beneficial of femtocelltechnology deployment and the mathematical model for mobile user connectivity are introduced

at section 4. Femtocell/macrocell network modeling and the interaction between outage

probability and spectral efficiency are presented in Section 5. In Section 6, the numerical resultsare discussed. Finally, the paper is concluded at Section 7.

2. RELATED WORK

Most of studies and researches in Femto-Macro cellular networks are focused on proposing the

schemes to overcome the technical challenges in such networks such as, interferencemanagement, handover control, spectrum allocation, access methods and etc. In [3], the authors

proposed an efficient hybrid frequency assignment technique based on interference limited

coverage area (ILCA). They studied two different scenarios of path loss for calculation ILCA.On the same direction the authors in [4] introduced a decentralized resource allocation scheme

for shared spectrum in macro/femto OFDMA networks in order to avoid inter-cell interference.In addition, the authors in [5] exploited the femto size feature to propose a resource reuse

scheme based on split reuse and graph theory. In sequel, the authors in [6] have proposed aradio resource management in self organizing femtocell and macrocell networks to satisfy the

demanding of selfish users. Further, according to the proposed scheme, they have introducedincentives for femtocell users to share their FAPs with public users.

On the other hand, the authors in [7] studied the outage probability in macrocell integrated with

femtocell CDMA networks. They concluded that femtocell exclusion region and a tier selectionbased handoff policy offers modest improvements in area spectral efficiency (ASE). The

handover procedure in femtocell integrated with 3GPP LTE network is analyzed for threedifferent scenarios: hand-in, hand-out and inter-FAP in [8]. Furthermore, the authors in [9] have

proposed a novel handover decision algorithm according to the location of user in the femtocellcoverage and at the same time taking into account the received signal strength (RSS) from

femtocell and macrocell. In [10] the authors have investigated the existing access methods forfemtocells with their benefits and drawbacks. They have also provided a description for

business model and technical impact of access methods in femto/macro networks. Subsequently,

a framework for femtocell access method of both licensed and unlicensed band with thecoexisting with WiFi is introduced in [11]. In addition, the conflict between open and close

access methods is compared in [12]. They focused on the downlink of femtocell networks and

they evaluated the average throughput as a function of SINR of home and cellular users for open

and closed access methods.

Unlike the above literature that mainly focus on introducing the solutions for challenges in

femtocell/macrocell networks. To the best of our knowledge, our work is able to provide aconvenient solution for computing the probability of connectivity in such networks. More

specifically, we propose an analytical model in femtocell/macrocell networks in order tocompute the probability of connectivity in terms of communication range, and mobility of

mobile users. As well as we study the interplays between the probability of outage and spectral

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efficiency in such networks. Further, we consider a femtocellular network based-open accessmethod (OAM) in order to enhance the macrocell users (MUEs) link reliability by selecting the

closest FAPs.

3. FEMTOCELL ACCESS METHODS

3.1. Closed Access Method (CAM)

In this scenario, the FAP serves only the authorized users, therefore the macro users are notallowed to access FAP. As portrait in Fig.1, although the macro user MUE1 or MUE3 is close

to the radio coverage of femtocell, they cannot access FAPs [1]. On the other hand, the femtousers (FUEs) prefer CAM for private access in order to protect privacy [12]. In sequel, the

femto users dont like to share the limited capacity of FAP with others if no cost revenue.However, deploying CAM causes severe cross-tier interference from macro users in the reverse

link or to nearby macro users in forward link. Therefore, interference mitigation and spectrummanagement are technical challenges in CAM [2].

3.2. Open Access Method (OAM)

In order to reduce the cross-tier interferences the OAM is considered. In OAM any passing

macro user can access a FAP if the macro user is within the radio coverage of femtocell.Alternatively the macro user MUE1 or MUE3 causes or experiences strong interference, they

can access FAP as shown in Fig.2. Therefore, OAM is more efficient in improving systemcapacity because OAM is able to serve the macro users that causing interferences. However,

OAM introduces an enormous number of handover requests and consequently highcommunication overhead on both the radio access networks (RAN) and IP core networks (CN)

[1]. In our system model, we considered the OAM method since we would gain not onlyimproving system capacity but also reducing interferences. On the other hand, the handover

problems can be solved by handover control mechanism.

3.3. Hybrid Access Method (HAM)

As we have seen previously all access methods suffer from pros and cons. Hybrid access

method (HAM) is considered an adaptive method between OAM and CAM [2]. In HAM aportion of FAP resources are reserved for exclusive use of the CAM and the remaining

resources are assigned in an open manners; thereby the outage number of users in macrocell can

be reduced. This procedure should be controlled to avoid high blocking probability in femtocelland to reduce the annoying of registered users [12]. Nowadays, Femto forum, Broadband forum

and 3GPP specifications try to finish the most efficient access method in femtocell networks butit is still under scrutiny.

text

MUE1

MUE2

MUE3

FUE3

FUE1

FUE2

MBS

FAP

FAP

FAP

Figure 1. Closed access method (CAM) scenario.

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Figure 2. Closed access method (CAM) scenario.

4.BENEFITSOFDEPLOYMENTFEMTOCELLSTECHNOLOGY

Femtocells are self-organized networks (SONs) that are integrating itself into the mobilenetwork without user intervention and then reducing deployment cost [20]. One of the keyfeatures of deployment the femtocells technology integrated with the current mobile cellularnetworks is that FUE or MUE requires no new equipment and hence femtocells technology does

not require dual-mode handset [21]. Furthermore, the femtocell networks are capable of servingthe remote areas with no coverage or poor signal as well as reducing the traffic volume on the

macrocell. Therefore in terms of the communication range and the mobility factor of mobileusers, in the following subsection, we introduce a tractable mathematical model for connectivity

probability of mobile user.

4.1. Analytical Model for mobile user connectivity

We consider a scenario of a femtocells network; the mobile users are randomly and uniformly

distributed in its coverage area. In addition, we assume a femtocells network is deployed withinthe communication range of a macrocell base station (MBS) and is allowed open access method(OAM) in order to enhance the mobile users (MUE) link reliability by selecting the closest

FAPs.

We assume that the coverage area of femtocell is a circle with unity radius and a particular

MUE with a communication range r(r

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The disconnectivity defined as the probability of at least one MUE being out of coverage regionof all other femtocells in a given macrocell. The probability of MUE being in disconnectivity

may be determined by calculating the area of intersection between a circle of unity radius andcircle of radius ras follows:

2

0, 1

( , ) ( , ), 1 1

1

A r h r

r

= <

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Assuming that there areNf number of femtocells overlaid in the macrocell mobile network.Hence, the probability of MUE is not able to connect to any femtocell amongNfbeing (Pj) isgiven by the probability that allNf-1femtocells lie in uncovered region. Then

1 1

( , ) ( , )1

f fN N

j jj

S A r A r PS S

= =

(7)

where S= ,j=1, 2,, Nf is the area of the circle with unity radius for all femtocells. Thereby,

the probability of at least one MUE being disconnected ( 1dP ) is given by

1

1

fN

d xxP P

==U . Upper

bound on 1d

P can be obtained by using the union bound definition as

1

1

1

( , )1

ff

NN

j

d

x

A rP

S

=

=

(8)

By using (5)

1

1 ( , )1

fN

d

A rP

(9)

Thereby, we can obtain the probability of connectivity (C

P ) as the complement of

disconnectivity probability of at least one MUE being isolated ( 1dP ), hence from (9), we obtain

1( , )

1 1fN

C

A rP

(10)

5.FEMTOCELL/MACROCELLNETWORKMODELING

We consider a network scenario of open access method (OAM) in the hierarchical macrocellwith highly dense femtocells as depicted in Fig.4, whereNf femtocells are uniformly distributed

in the macrocell. The density of FAPs and the density of users are represented by Df (FAPs/m2)

and Du (users/m

2

) respectively. We assume Du is a random stochastic Poisson process followsspatial distribution [13]. A simplified wireless channel model is considered in our network

model (i.e., fading, shadowing, noise etc. is neglected), since the channel model is a

distance-dependent according to the path loss with exponent >2. Subsequently, considering allusers transmit with a fixed power Ptand all FAPs have the same power level of sensitivity, Pmin.Thereby, we can express the communication range rin the reverse link as

1/

min

tP

rP

=

(11)

Furthermore, the mobile users usually try to connect to the closest FAP by sending a call

request. The request may be accepted or rejected according to the available capacity in the FAPor the users are not inside the FAP coverages range [14]. The rejected requests may be servedby the overlay macrocell. Without loss of generality, we are not focusing on capacity issue inthis study. We consider an OAM as access method to reduce the cross-tier interference between

femtocell and macrocell usage [15]. Thereby in our analysis, the mobile user is referred tofemtocell user (FUE) or macrocell user (MUE). Therefore, the probability of a given user is

fully connected (PC) to the FAP is defined as the ratio:

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,f active

C

u

DP

D=

(12)

whereDf,active denote to the density of active FAPs or defined as the density of active channels in

a respective FAP. Therefore, PCcan be approximated as follows [14]:

( )21 exp 1 exp( )ufC fu f

DDP D r

D D

=

(13)

Additionally, we study the effect of interference between the active FAP and mobile users interms of outage probability [16], [17] and [18]; we consider the signal to interference (SIR) is

given by:

0

0 i

t

t

i

P rS IR

N P r

=

+

(14)

where r0 represents to the distance between the reference FAP and its respective mobile user, is the set of the interferer users,N0 represents the noise power and ri is the distance between theith interferer at the reference FAP. Thereby, the outage probability (Poutage) is defined as the

probability of FAP experiences a SIR less than or equal to a given threshold [19], i.e.

Pr{ }outageP SIR = (15)

Hence, Poutage can be expressed as:

( )( )( ) ( )

2/ 2

,

2/ 2

,

1 exp1

1 exp

f f activ e f

outage

f activ e f f

D D D rP

D D D r

+ =

+

(16)

The evaluation of the minimum value on the outage probability is occurred at the SIR threshold

. Under the usual assumption in interference-limited networks, the noise power is negligible

and the overall interference power is treated as Gaussian noise, hence the minimum SIR ratio

required to guarantee a given spectral efficiency (bits/sec. Hz) at each active link can becalculated by using the Shannons capacity formula, which yields

2 1 = (17)

Figure 4. Femtocell/Macrocell mobile networks.

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6.NUMERICAL RESULTS

In this section, we present the numerical results of mobile user connectivity infemtocell/macrocell networks. The proposed analytical model has been the basis for the

implementation of network model. Different input parameters for the network model are setting

according to the real cellular networks. With the aid of Mathematica packages, we obtain somenumerical solution and graphical illustrations for all metrics of interest, i.e. the probability of

connectivity outage probability, and spectral efficiency.

6.1. Mobile user connectivity Probability

The user connectivity probability given by (9) is function of mobility factor (), communicationrange (r) and number of femtocells (Nf). We evaluate the behavior of the proposed model undertwo different number of femtocellsNf=100 andNf=10. Fig.5 and Fig.6 illustrate the probabilityof mobile user connectivity. As figures indicate, the connectivity probability increases by

increasing the communication range especially when the mobility factor () is varied from 1towards -1, i.e., the mobile users moved from outside to inside of femtocell. In contrast, the

connectivity probability decreases when the mobility factor is varied from -1 towards 1. Also,

we can observe that the probability of connectivity is increased when the number of femtocellsis high. This is due to when the macrocell is highly dense with femtocells, the probability of

mobile user connectivity increases. In sequel, Fig.7 concludes the above discussion.

Figure 5. Pc versusand ratNf=100.

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Figure 6 Pc versusand ratNf=10.

Figure 7 Pc versus rat different values ofand Nf.

6.2. Outage probability and spectral efficiency

In this section, we study the performance of the connectivity probability (PC), outage probability

(Poutage) and the spectral efficiency () at different values of femtocell density (Df) and userdensity (Du).

We present the results ofPC as a function of the density of users (Du) at different values of

femtocells densities (Df) and at fixed communication range as shown in Fig.8. Femtocell density

is produced different instances of the problem. As the figure indicates when the density offemtocells increases the user connectivity probability increases. However, when the density of

users (Du) increases, the user connectivity probability decreases. This is due to when the numberof users which access the same FAP are increased, i.e., increasing the number of the rejected

users, hence the user connectivity probability is decreased. In other word, the performance offemtocell/macrocell networks is significantly improved with increasing the density of

femtocells.

Fig.9 shows the outage probability versus the density of femtocells at different user densities in

femtocell/macrocell networks. We assumed the desired spectral efficiency in the network is

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=2bits/s.Hz and the communication range is computed as in (10) at =4, Pt=1, Pmin=10.Obviously, Pout is steadily increases at lower density of femtocells, while Pout decreases whenthe density of femtocells increased. Also, we observe Pout is significantly decreased after Df=2

FAPs/m2

for different values of users density.

On the other hand, we study the performance of spectral efficiency () in femtocell/macrocellnetworks for achieving a given threshold value of outage probability (Pout). Fig. 10 illustrates

the spectral efficiency () in bits/s.Hz when the user density increasing. As expected, thespectral efficiency decreases when the user density increases, this is due to increasing the

number of users that used transmission channel. Obviously, at different threshold values of

outage probability, we can get different plots of . However, the performance of spectral

efficiency is increased to achieve the desired Pout. In other word, the plots of are increasedwhen the required Pout is high. This is probably occurred when the number of outage users

increased, the channel sends with high capacity (i.e. high ) and at the same time it satisfies thedesired Pout.

Figure 8. Pc versusDu at different values ofDf.

Figure 9. PoutageversusDfat different valuesofDu.

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Figure 10. versusDu at different threshold Poutage.

To summarize, our analysis shows that, the probability of mobile user connectivity depends on

different parameters such as communication range, femtocell density, and user density. It is

shown that large number of femtocells in macrocell guaranteed feasible connectivity probability

in Femto/Macro cellular networks.

7.CONCLUSIONS

This paper presented an analytical model framework for computing the probability of mobile

user connectivity in femtocell/macrocell networks. The performance of the connectivityprobability is measured in terms of communication range, mobility factor, user density and

femtocell density. In addition, we examined the performance of outage probability and spectral

efficiency in such network. Our studies demonstrated that the computing of user connectivityprobability is essentially efficient during planning the Macrocellular networks integrated with

Femtocellular networks.

ACKNOWLEDGMENTS

This work was supported by the Deanship of Scientific Research in Salman Bin Abdulaziz

University, Kingdom of Saudi Arabia under Grants No.20/ /1432.

REFERENCES

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[5] Yongsheng S, MacKenzie A., DaSilva L.A, Ghaboosi K., and Latva-aho M., On Resource Reusefor Cellular Networks with Femto- and Macrocell Coexistence Proc. IEEE Globecom, Dec. 2010,pp.1-6.

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[6] C. Han Ko and H. Yu Wei, On-Demand Resource-Sharing Mechanism Design in Two-TierOFDMA Femtocell Networks, IEEE Trans. on Vehicular. Tech., Vol. 60, No. 3, March 2011,p.p.1059-1071.

[7] Chandrasekhar V. and Andrews J, Uplink capacity and interference avoidance for two-tierfemtocell networks, IEEE Trans. Wireless Comm, Vol. 8 No. 7, July 2009, pp. 3498 3509.

[8] Ardian U., Robert B. and Melvi U., Handover procedure and decision strategy in LTE-basedfemtocell network, Springer Telecommunication Systems, Online First, Sept. 2011.

[9] Jung-Min M. and Dong-Ho C., Novel Handoff Decision Algorithm in Hierarchical Macro/Femto-Cell Networks in Proc. IEEE WCNC, April 2010, pp. 1-6.[10] A. Golaup, M. Mustapha, and L. Boonchin, Access control mechanisms for femtocells,, IEEE

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[11] Feilu L., Bala E., Erkip E., and Rui Y., A framework for femtocells to access both licensed andunlicensed bands Proc. IEEE WiOpt, May 2011, pp.407-4011.

[12] Han-Shin J., Ping X. and Andrews J., Downlink Femtocell Networks: Open or Closed? Proc. IEEEICC, June 2011, pp.1-65.

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Authors Biographies

Saied M. Abd El-atty received the B.S. and M.S. degrees from Menoufia

University, Faculty of Electronic Engineering, in 1995 and 2001, all in Electronics

& Communications Engineering respectively. He received the PhD degree in

Wireless Communication Networks from University of Aegean (UOA) at theInformation and Communication Systems Engineering Department, Greece, Samos

in 2008. He is a member of the faculty members in the department of Electronics

and Electrical Communication at Faculty of Electronic Engineering, Menouf,

Egypt. Currently, he is working as assistant professor in Salman Bin Abulaziz

University, KSA. He is the head of computer science and information department in Science College. Dr.

Saieds current research interests include design, analysis, and optimization of wireless mobile

communication networks and vehicular networks as well as cognitive radio systems.

Zakaria M. M. Gharsseldien received his B.Sc. degree, M.S. degrees, and Ph.D.

degree in Applied Mathematics from Al-Azhar University, Cairo, Egypt, in

1992.,1998, and 2003, respectively. He worked as a Lecturer in Department of

Mathematics, Faculty of Science, Cairo, Al-Azhar University from 2003 to 2007.

He is currently an Assistant Professor with the Department of Mathematics ,

Faculty of Arts and Science (Wadi Addwassir), Salman Bin AbdulAziz Universityfrom 2007. His current research interests is mathematical modeling in biology,

medicine, and wireless communications, biomathematics ,and bio fluid mechanics.

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